FYI, I've stopped work on this PR.
I ended up rolling my own simple component that allowed me to do what I wanted to do in about 70 lines of code. I was able to get away with ignoring coef_ for multi-output y because I simply don't need to handle that case and figuring out what that entails.

I don't currently have the time/inclination to figure out exactly what needs to get done in order to make the tests handle sparse matrices and whatnot.

Thanks for checking in and for your work so far.

Also, I'd be fine to see this without multi-output support. The non-validation of X is more often useful, but it needs to be tested.

This is no longer necessary. Superceded by #11635 .